Steiner surface

In geometry, a branch of mathematics, the Steiner surfaces, discovered by Jakob Steiner, are mappings of the real projective plane into three-dimensional real projective space. They are the linear projection of the Veronese surface, an embedding of the real projective plane into five-dimensional projective space, onto three-dimensional projective space.

The Steiner surfaces can be classified into ten different types, including the Roman surface and the cross-cap.

References

• A. Coffman, A. Schwartz, and C. Stanton: The Algebra and Geometry of Steiner and other Quadratically Parametrizable Surfaces. In Computer Aided Geometric Design (3) 13 (April 1996), p. 257-286
• Bert Jüttler, Ragni Piene: Geometric Modeling and Algebraic Geometry. Springer 2008, ISBN 9783540721840, p. 30 (restricted online copy at Google Books)

External links

• Coffman Steiner Surfaces, englisch
• Weisstein, Eric W., "Steiner Surface" from MathWorld.